MinT - Best Known (75, ∞, s)-Nets in Base 4

Best Known (75, ∞, s)-Nets in Base 4

Digital (75, m, 104)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (75, 103)-sequence over F₄, using
- t-expansion [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Digital (75, m, 112)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (75, 111)-sequence over F₄, using
- t-expansion [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

There is no (75, m, 241)-net in base 4 for arbitrarily large m, because

m-reduction [i] would yield (75, 959, 241)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4⁹⁵⁹, 241, S₄, 4, 884), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 8262 489630 728655 302275 878141 541992 389190 244945 217605 156623 683200 760909 466942 554947 134203 504523 936136 407046 549809 754251 246153 853559 681108 576851 314347 926981 716697 909245 193601 206716 186815 920484 715002 525011 962236 645040 739107 711844 384467 314993 374557 838254 141998 102134 564748 837304 760623 083054 549834 622667 026394 429849 273274 989421 908447 760207 628457 176822 503539 954838 672925 348198 375192 139049 760253 761263 520665 760291 988070 512092 157044 246032 414117 458582 129230 183970 154037 279232 937241 259015 965741 782819 776004 577390 643283 188754 692675 315465 672700 270149 292703 057801 408121 528599 267473 834599 514112 / 295 > 4⁹⁵⁹ [i]